6533b7d6fe1ef96bd1266fc6
RESEARCH PRODUCT
The algebraic structure of cohomological field theory
Danny BirminghamMark Rakowskisubject
Pure mathematicsTopological quantum field theoryDifferential formAlgebraic structureGeneral Physics and AstronomyCodimensionModuli spaceAlgebraOperator algebraQuantum gravityGeometry and TopologyOperator product expansionMathematical PhysicsGeneral Theoretical PhysicsMathematicsdescription
Abstract The algebraic foundation of cohomological field theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occuring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1993-06-01 |